In a geometric sequence, the common ratio \( r \) is the factor by which we multiply each term to get the next term.
Given the recursively defined geometric sequence:
- The first term \( a_1 = 56 \)
- The recursive definition \( a_n = 4a_{n-1} \)
From the recursive relation, we can see that each term is obtained by multiplying the previous term by 4.
Thus, the common ratio \( r \) for this geometric sequence is:
\[ r = 4 \]
Therefore, the common ratio of the sequence is \( 4 \).